Well, I have survived to tell this tale....
LHR T5 to TXL Friday 28 August, return journey Friday 4 September.
No attempt at distancing by BA, both flights were full (maybe 1 or 2 empty seats, but middle seats were being used).
Plane boarded and deplaned by rows of 5 seats, from the back to embark and from the front to disembark. On landing both times , a few people did stand up and attempt to retrieve luggage fom overhead bins but announcements were made reminding them to stay seated until their row number was called.
Check-in time was 2 hours in advance of departure time but this was excessive due to reduced numbers at both airports; due to traffic issues on the M25 I arrived about 1 1/2 hours before departure from Heathrow and almost exactly the 2 hours at Tegel ... plenty of time to kill until boarding. Most but not all shops are open at Heathrow T5 but with a limit on numbers of people permitted at any one time (as expected) but this wasn't an issue... personally I find the barriers and security staff at the shop entrances off-putting (not just at Heathrow but in town centres too).
Tegel - on the basis that there are few passengers and that the airport is scheduled top close in the near future, not all the shops were open but I reckon that over half were. No facility to get "free" water from a fountain once through security/emigration. Only way would be to buy from kiosk or machine (TXL has its own, pratically unique way of doing things).
Immigration at Heathrow T5 is a farce, the queue snakes back and forth on itself so not possible to observe social distancing. No requirement to self-isolate when arriving from Germany, but those in the queue around you could be from countries where the virus is rampant. As per about 50-% of occasions, the auto-gate dd not work for me, so further queueing to see an Officer who was pleasant and efficient, and I was asked to show my Locator Form on my smart phone (and he scanned it). By the time this was dealt with, my case was already on the luggage belt. Only one exit was open to get into the terminal though, and of course it was the furthest one from where our bags were delivered.
Nevertheless, not too bad an experience at both ends... around an hour from airport to hotel in Berlin (by TXL bus then tram, both of which were about 1/3 full), and around an hour to get home from T5 (by my car).
My biggest concern was the passenger next to me on my return flight - wearing an athletics vest top, and shorts. Totally inappropriate clothing at the best of times IMHO, but in these times, potential for "fluid contact" via sweat from bare skin is much increased.